JEE Main 2023 · 1 February · morning · Single correct · +4 / −1
The average kinetic energy of a molecule of the gas is
- (a) proportional to volume
- (b) dependent on the nature of the gas
- (c) proportional to absolute temperature
- (d) proportional to pressure
Answer and solution
Answer (c) proportional to absolute temperature
Solution
Physics sir · 4 steps
Temperature measures the average KE of the molecules, so that energy depends on T and nothing else.
- From kinetic theory. Kinetic theory gives pV = 1/3 N m v̅²̅ for N molecules. The ideal gas law gives pV = N k_B T. Equate the two right-hand sides.
K̅E̅ = 1/2 m v̅²̅ = 3/2 k_B T
- Read the result. Only T and the universal constant k_B are left. Pressure, volume and the molecular mass m have all dropped out.
- Check p and V. Halve the volume at fixed temperature and the pressure doubles, yet K̅E̅ does not change. So it cannot be proportional to either p or V.
- So. The average kinetic energy of a molecule is proportional to the absolute temperature, option (c).
The idea to keep. Average translational KE per molecule is 3/2k_BT for every ideal gas. Heavier molecules move slower, so m cancels out and only T matters.
Answer from the NTA final answer key. Solution by PrepWiser.